Abstract
In the variable-sized online bin packing problem, one has to assign items to bins one by one. The bins are drawn from some fixed set of sizes, and the goal is to minimize the sum of the sizes of the bins used. We present new algorithms for this problem and show upper bounds for them which improve on the best previous upper bounds. We also show the first general lower bounds for this problem. The case where bins of two sizes, 1 and α ∈ (0,1), are used is studied in detail. This investigation leads us to the discovery of several interesting fractal-like curves. Our techniques are also applicable to the closely related resource augmented online bin packing problem, where we have also obtained the first general lower bounds.
Research supported by Israel Science Foundation (grant no. 250/01).
Research supported by the Louisiana Board of Regents Research Competitiveness Subprogram.
This work done while the author was at the CWI, The Netherlands. Research supported by the Netherlands Organization for Scientific Research (NWO), project number SION 612-30-002.
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References
Brown, D. J. A lower bound for on-line one-dimensional bin packing algorithms. Tech. Rep. R-864, Coordinated Sci. Lab., University of Illinois at Urbana-Champaign, 1979.
Chandra, B. Does randomization help in on-line bin packing? Information Processing Letters 43, 1 (Aug 1992), 15–19.
Coffman, E. G., Garey, M. R., AND Johnson, D. S. Approximation algorithms for bin packing: A survey. In Approximation Algorithms for NP-hard Problems, D. Hochbaum, Ed. PWS Publishing Company, 1997, ch. 2.
Csirik, J. An on-line algorithm for variable-sized bin packing. Acta Informatica 26, 8 (1989), 697–709.
Csirik, J., AND Woeginger, G. On-line packing and covering problems. In On-Line Algorithms—The State of the Art, A. Fiat and G. Woeginger, Eds., Lecture Notes in Computer Science. Springer-Verlag, 1998, ch. 7.
Csirik, J., AND Woeginger, G. Resource augmentation for online bounded space bin packing. In Proceedings of the 27th International Colloquium on Automata, Languages and Programming (Jul 2000), pp. 296–304.
Epstein, L., Seiden, S. S., AND Van Stee, R. On the fractal beauty of bin-packing. Tech. Rep. SEN-R0104, CWI, Amsterdam, 2001.
Friesen, D. K., AND Langston, M. A. A storage-size selection problem. Information Processing Letters 18 (1984), 295–296.
Friesen, D. K., AND Langston, M. A. Variable sized bin packing. SIAM Journal on Computing 15 (1986), 222–230.
Johnson, D. S.Near-optimal bin packing algorithms. PhD thesis, Massachusetts Institute of Technology, Cambridge, Massachusetts, 1973.
Johnson, D. S. Fast algorithms for bin packing. Journal Computer Systems Science 8 (1974), 272–314.
Johnson, D. S., Demers, A., Ullman, J. D., Garey, M. R., AND Graham, R. L. Worst-case performance bounds for simple one-dimensional packing algorithms. SIAM Journal on Computing 3 (1974), 256–278.
Kinnersley, N., AND Langston, M. Online variable-sized bin packing. Discrete Applied Mathematics 22, 2 (Feb 1989), 143–148.
Lee, C., AND Lee, D. A simple on-line bin-packing algorithm. Journal of the ACM 32, 3 (Jul 1985), 562–572.
Liang, F. M. A lower bound for online bin packing. Information Processing Letters 10 (1980), 76–79.
Ramanan, P., Brown, D., Lee, C., AND Lee, D. On-line bin packing in linear time. Journal of Algorithms 10, 3 (Sep 1989), 305–326.
Richey, M. B. Improved bounds for harmonic-based bin packing algorithms. Discrete Applied Mathematics 34 (1991), 203–227.
Seiden, S. S. An optimal online algorithm for bounded space variable-sized bin packing. In Proceedings of the 27th International Colloquium on Automata, Languages and Programming (Jul 2000), pp. 283–295.
Seiden, S. S. On the online bin packing problem. In Proceedings of the 28th International Colloquium on Automata, Languages and Programming (Jul 2001), pp. 237–249.
Van vliet, A. An improved lower bound for online bin packing algorithms. Information Processing Letters 43, 5 (Oct 1992), 277–284.
Yao, A. C. C. New algorithms for bin packing. Journal of the ACM 27 (1980), 207–227.
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Epstein, L., Seiden, S., van Stee, R. (2002). New Bounds for Variable-Sized and Resource Augmented Online Bin Packing. In: Widmayer, P., Eidenbenz, S., Triguero, F., Morales, R., Conejo, R., Hennessy, M. (eds) Automata, Languages and Programming. ICALP 2002. Lecture Notes in Computer Science, vol 2380. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45465-9_27
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DOI: https://doi.org/10.1007/3-540-45465-9_27
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